arXiv subjects

Yuqiong Wang

Publications and source records attributed to Yuqiong Wang.

10 recordsLinked to original sources

arXiv2026

Convex order and preservation of convexity for Bayesian posterior updates

We study how the response of a Bayesian posterior statistic to future observations changes as information accumulates. For a non-decreasing function $T$, define $Π_n^T=\E[T(Θ)\vert \mathcal F_n]$, where $Θ$ has an arbitrary prior and the observations come from a one-parameter exponential family. Conditioning on the same current value of $Π^T$, we show that the posterior statistic after additional observations is larger in convex order when the current posterior is based on fewer observations. We also prove preservation of convexity: the expected value of a convex function of the future posterior statistic is convex in the current posterior statistic. Together, these two properties provide structural tools for establishing time-monotonicity results in dynamic Bayesian decision and optimal stopping problems. If the exponential family contains an infinitely divisible distribution, the results extend to a continuous-time observation model through a family of Lévy processes.

math.ST↗

arXiv2026

Tractable bank capital structure: optimal control under Basel III constraints

Banks must optimize risky investments, dividend payouts, and capital structure under tight Basel III solvency and liquidity constraints, while costly equity issuance serves as a distress-recovery tool. We formulate this as a stochastic control problem that reduces the high-dimensional balance-sheet dynamics to a tractable one-dimensional process in the asset-to-deposit ratio, with state-dependent investment limits. The resulting policy is simple and interpretable: pay dividends at an upper reflection barrier and, when needed, recapitalize only at the distress boundary, jumping to an optimal target level. We characterize these thresholds analytically and show their sensitivity to regulatory parameters. From a regulatory viewpoint, we use Monte Carlo simulation to solve an outer optimization problem and map the efficient frontier between shareholder value and survival probability, both with and without a leverage cap. In the illustrative parameter ranges studied here, tightening solvency requirements often yields the best safety--profitability trade-off.

math.OC↗

arXiv2026

On hypoellipticity of degenerate operators in testing and detection problems

We study a class of degenerate diffusion generators arising in sequential testing and quickest detection problems with partial information. The observation process is driven by $k$ independent Brownian motions, while the hidden state takes $n+1$ values, with $k<n$. After transforming to posterior likelihood coordinates, we analyze Hörmander's condition both in the absence of state switching (testing) and in its presence (detection). We characterize hypoellipticity in the testing case and give explicit sufficient conditions in the detection case. We further study the stationary posterior operator, its parabolic extension, the joint observation-posterior operator, and its parabolic extension; their Hörmander conditions need not coincide. We characterize the relationships among these operators under our main structural regimes and discuss their probabilistic consequences and the regularity of the associated optimal stopping problem.

math.ST↗

arXiv2026

The relative efficiency of sequential tests

While many statistical procedures rely on a fixed sample size, sequential methods allow a decision-maker to adapt the sample size to achieve a given precision. In this way, sequential tests reduce the average number of observations required to achieve a given power of the test -- but by how much? To address this question, we focus on the scenario of testing the unknown drift of a Brownian motion, comparing the Wald sequential probability ratio test with tests that use a pre-determined fixed sample size. We provide precise bounds on the average reduction in sample size needed to achieve a desired precision. Specifically, we demonstrate that for symmetric error bounds, the sequential test reduces the average sample size by at least 36\% and by at most 75\%. Moreover, the reduction in sample size increases monotonically with the power of the test, meaning that the relative advantage of using a sequential test over a fixed sample size test grows as higher power is required. We also study the relative efficiency in the case with asymmetric error bounds, and we provide a lower bound in terms of the symmetric case.

math.ST↗

arXiv2026

Thompson Sampling Algorithm for Stochastic Games

We study a stochastic differential game with $N$ competitive players in a linear-quadratic framework with ergodic cost, where $d$-dimensional diffusion processes govern the state dynamics with an unknown common drift (matrix). Assuming a Gaussian prior on the drift, we use filtering techniques to update its posterior estimates. Based on these estimates, we propose a Thompson-sampling-based algorithm with dynamic episode lengths to approximate strategies. We show that the Bayesian regret for each player has an error bound of order $O(\sqrt{T\log(T)})$, where $T$ is the time-horizon, independent of the number of players. This implies that average regret per unit time goes to zero. Finally, we prove that the algorithm results in a Nash equilibrium.

math.OC↗

arXiv2024

Dynkin ghost games with asymmetry and consolation

We study a stopping game of preemption type between two players who both act under uncertain competition. In this framework we introduce, and study the effect of, (i) asymmetry of payoffs, allowing e.g. for different investment costs, and (ii) consolation, i.e. partial compensation to the forestalled stopper. In general, this setting does not offer an explicit equilibrium. Instead, we provide a general verification theorem, which we then use to explore various situations in which a solution can be constructed so that an equilibrium is obtained.

math.PR↗

arXiv2022

Stopping problems with an unknown state

We extend the classical setting of an optimal stopping problem under full information to include for problems with an unknown state. The framework allows the unknown state to influence (i) the drift of the underlying process, (ii) the payoff functions, and (iii) the distribution of the time horizon. Since the stopper is assumed to observe the underlying process and the random horizon, this is a two-source learning problem. Assigning a prior distribution for the unknown state, filtering theory can be used to embed the problem in a Markovian framework, and we thus reduce the problem with incomplete information to a problem with complete information but with one more state-variable. We provide a convenient formulation of the reduced problem, based on a measure change technique that decouples the underlying process from the state variable representing the posterior of the unknown state. Moreover, we show by means of several new examples that this reduced formulation can be used to solve problems explicitly.

math.PR↗

arXiv2022

Asymptotic mean value formulas, nonlocal space-time parabolic operators and anomalous tug-of-war games

The fractional heat operator $(\partial_t-Δ_x)^s$ and Continuous Time Random Walks (CTRWs) are interesting and sophisticated mathematical models that can describe complex anomalous systems. In this paper, we prove asymptotic mean value representation formulas for functions with respect to $(\partial_t-Δ_x)^s$ and we introduce new nonlocal, nonlinear parabolic operators related to a tug-of-war which accounts for waiting times and space-time couplings. These nonlocal, nonlinear parabolic operators and equations can be seen as nonlocal versions of the evolutionary infinity Laplace operator.

math.AP↗

arXiv2021

Bayesian sequential composite hypothesis testing in discrete time

We study the sequential testing problem of two alternative hypotheses regarding an unknown parameter in an exponential family when observations are costly. In a Bayesian setting, the problem can be embedded in a Markovian framework. Using the conditional probability of one of the hypotheses as the underlying spatial variable, we show that the cost function is concave and that the posterior distribution becomes more concentrated as time goes on. Moreover, we study time monotonicity of the value function. For a large class of model specifications, the cost function is non-decreasing in time, and the optimal stopping boundaries are thus monotone.

math.ST↗

arXiv2020

Multi-dimensional sequential testing and detection

We study extensions to higher dimensions of the classical Bayesian sequential testing and detection problems for Brownian motion. In the main result we show that, for a large class of problem formulations, the cost function is unilaterally concave. This concavity result is then used to deduce structural properties for the continuation and stopping regions in specific examples.

math.PR↗